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Glossary

ABC notation A text-based musical notation for folk and traditional music.

Accompaniment The musical part which provides the rhythmic and/or harmonicsupport for the melody or main themes of a song or instrumental piece. There aremany different styles and types of accompaniment in different genres and styles ofmusic. Examples are: an harmony accompaniment through a progression (sequence)of chords to be played by a polyphonic instrument such as a piano or guitar, and acounterpoint accompaniment through a sequence of melodic voices to be played byhuman voices or by instruments.

Activation function The function associated to a neural network layer. In the caseof hidden layers, its purpose is to add nonlinearity. Standard examples are sigmoid,tanh and ReLU. In the case of the output layer, its purpose is to organize the resultin order to be able to interpret it. Examples of output layer activation function are:softmax for computing associated probabilities in the case of a categorical classifi-cation task with a single label to be selected, and identity in the case of a predictiontask.

Algorithmic composition The use of algorithms and computers to generate musiccompositions (symbolic form) or music pieces (audio form). Examples of modelsand algorithms are: grammars, rules, stochastic processes (e.g., Markov chains),evolutionary methods and artificial neural networks.

Architecture An (artificial neural network) architecture is the structure of the or-ganization of computational units (neurons), usually grouped in layers, and theirweighted connexions. Examples of types of architecture are: feedforward (aka mul-tilayer Perceptron), recurrent (RNN), autoencoder and generative adversarial net-works. Architectures process encoded representations (in our case of a musical con-tent) which have been encoded.

Artificial neural network A family of bio-inspired machine learning algorithmswhose model is based on weighted connexions between computing units (neurons).

263J.-P. Briot et al., Deep Learning Techniques for Music Generation, Computational

Synthesis and Creative Systems, https://doi.org/10.1007/978-3-319-70163-9

© Springer Nature Switzerland AG 2020

264 Glossary

Weights are incrementally adjusted during the training phase in order for the modelto fit the data (examples).

Attention mechanism A mechanism inspired by the human visual system whichfocuses at each time step on some specific elements of the input sequence. This ismodeled by weighted connexions onto the sequence elements (or onto the sequenceof hidden units) which are subject to be learned.

Autoencoder A specific case of artificial neural network architecture with an out-put layer mirroring the input layer and with a hidden layer. Autoencoders are goodat extracting features.

Backpropagation A short hand for “backpropagation of errors”, it is the algorithmused to compute the gradients (partial derivatives with respect to each weight pa-rameter and to the bias) of the cost function. Gradients will be used to guide theminimization of the cost function in order to fit the data.

Bag-of-words (BOW) It consists in transforming the original text (or arbitrary rep-resentation) into a vocabulary composed of all occurring tokens (items). Then, var-ious measures can be used to characterize the text, the most common being termfrequency, i.e. the number of times a term appears in the text. It is mainly used forfeature extraction, e.g., to characterize and compare texts.

Bias The b offset term of a simple linear regression model h(x) = b+ θx and byextension of a neural network layer.

Bias node The node of a neural network layer corresponding to a bias. Its constantvalue is 1 and is usually notated as +1.

Binning A technique to discretize a continuous interval or to reduce the dimen-sionality of a discrete interval. It consists of dividing the original domain of valuesinto smaller intervals and replacing each bin (and the values within it) by a valuerepresentative, often the central value.

Bottleneck hidden layer (aka Innermost hidden layer) The innermost hiddenlayer of a stacked autoencoder. It provides a compact and high-level embedding ofinput data and may be used as a seed for generation (by the chain of decoders).

Challenge One of the qualities (requirements) that may be desired for music gen-eration. Examples of challenges are: incrementality, originality and structure.

Chromagram (aka Chroma) A discretized version of a spectrogram. It is dis-cretized onto the tempered scale and is independent of the octave.

Classification A machine learning task about the attribution of an instance to aclass (from a set of possible classes). An example is to determine if next note is aC4, a C�4, etc.

Compound architecture An artificial neural network architecture which is the re-sult of some combination of some architectures. Examples of types of combinationare composition, nesting and pattern instantiation.

Glossary 265

Conditioning architecture The parametrization of an artificial neural network ar-chitecture by some conditioning information (e.g., a bass line, a chord progres-sion. . . ) represented via a specific extra input, in order to guide the generation.

Connexion A relation between a neuron and another neuron representing a com-putational flow from the output of the first neuron to an input of the second neuron.A connexion is modulated by a weight which will be adjusted during the trainingphase.

Convolution In mathematics, a mathematical operation on two functions sharingthe same domain that produces a third function which is the integral (or the sum inthe discrete case – the case of images made of pixels) of the pointwise multiplicationof the two functions varying within the domain in an opposing way. Inspired both bymathematical convolution and by a model of human visions, it has been adapted toartificial neural networks and it improves pattern recognition accuracy by exploitingthe spatial local correlation present in natural images. The basic principle is to slidea matrix (named a filter, a kernel or a feature detector) through the entire image (seenas the input matrix), and for each mapping position to compute the dot product ofthe filter with each mapped portion of the image and then sum up all elements of theresulting matrix. The results are named feature maps.

Correlation Any statistical relationship, whether causal or not, between two ran-dom variables. Artificial neural networks are good at extracting correlations be-tween variables, for instance between input variables and output variables and alsobetween input variables.

Cost function (aka Loss function) The function used for measuring the distancebetween the prediction by an artificial neural network architecture (y) and the actualtarget (true value y). Various cost functions may be used, depending on the task(prediction or classification) and the encoding of the output, e.g., mean squarederror, binary cross-entropy and categorical cross entropy.

Counterpoint In musical theory, an approach for the accompaniment of a melodythrough a set of other melodies (voices). An example is a chorale with 3 voices(alto, tenor and bass) matching a soprano melody. Counterpoint focuses on the hori-zontal relations between successive notes for each simultaneous melody (voice) andthen considers the vertical relations between their progression (e.g., to avoid parallelfifths).

Cross-entropy A function measuring the dissimilarity between two probabilitydistributions. It is used as a cost (loss) function for a classification task to measurethe difference between the prediction by an artificial neural network architecture (y)and the actual target (true value y). There are two types of cross-entropy cost func-tions: binary cross-entropy when the classification is binary and categorical cross-entropy when the classification is multiclass with a single label to be selected.

Data synthesis A machine learning technique to generate synthetic data as a wayto artificially augment the size of the dataset (the number of training examples), in

266 Glossary

order to improve accuracy and generalization of the learnt model. In the musicaldomain, a natural and easy way is transposition, i.e. to transpose all examples in allkeys.

Dataset The set of examples used for training an artificial neural network architec-ture. The dataset is usually divided into two subsets: the training set used during thetraining phase and the validation set used to estimate the ability for generalizationby the model learnt.

Decoder The decoding component of an autoencoder which reconstructs the com-pressed representation (an embedding) from the hidden layer into a representationat the output layer as close as possible to the initial data representation at the inputlayer.

Decoder feedforward strategy A strategy for generating content based on an au-toencoder architecture in which values are assigned onto the latent variables of thehidden layer and forwarded into the decoder component of the architecture in orderto generate a musical content corresponding to the abstract description inserted.

Deep learning (aka Deep neural network) An artificial neural network architec-ture with a significant number of successive layers.

Discriminator The discriminative model component of generative adversarial net-works (GAN) which estimates the probability that a sample came from the real datarather than from the generator.

Embedding In mathematics, an injective and structure-preserving mapping. Ini-tially used for natural language processing, it is now often used in deep learning asa general term for encoding a given representation into a vector representation.

Encoder The encoding component of an autoencoder which transforms the datarepresentation from the input layer into a compressed representation (an embedding)at the hidden layer.

Encoding The encoding of a representation consists in the mapping of the repre-sentation (composed of a set of variables, e.g., pitch or dynamics) into a set of inputs(also named input nodes or input variables) for the neural network architecture. Ex-amples of encoding strategies are: value encoding, one-hot encoding and many-hotencoding.

End-to-end architecture An artificial neural network architecture that processesthe raw unprocessed data – without any pre-processing, transformation of represen-tation, or extraction of features – to produce a final output.

Enharmony In the tempered system, the equivalence of notes with a same pitch,for example A� with B�, although harmonically they are distinct.

Feature map Also named a convolved feature, this is the result of applying a fil-ter matrix (also named a feature detector) at a specific position of an image and

Glossary 267

summing up all dot products. This represents the basic operation of a convolutionalartificial neural network architecture.

Feedforward The basic way for a neural network architecture to process an inputby feedforwarding the input data into the successive layers of neurons of the archi-tecture until producing the output. A feedforward neural architecture (also namedmultilayer neural network or multilayer Perceptron, MLP) is composed of succes-sive layers, with at least one hidden layer.

Fourier transform A transformation (which could be continuous or discrete) ofa signal into the decomposition into its elementary components (sinusoidal wave-forms). As well as compressing the information, its role is fundamental for musicalpurposes as it reveals the harmonic components of the signal.

Generative adversarial networks (GAN) A compound architecture composed oftwo component architectures, the generator and the discriminator, who are trainedsimultaneously with opposed objectives. The generator objective is to generate syn-thetic samples resembling real data while the discriminator objective is to detectsynthetic samples.

Generator The generative model component of generative adversarial networks(GAN) whose objective is to transform a random noise vector into a synthetic(faked) sample which resembles real samples drawn from a distribution of real data.

Gradient A partial derivative of the cost function with respect to a weight param-eter or a bias.

Gradient descent A basic algorithm for training a linear regression model and anartificial neural network. It consists in an incremental update of the weight parame-ters guided by the gradients of the cost function until reaching a minimum.

Harmony In musical theory, a system for organizing simultaneous notes. Harmonyfocuses on the vertical relations between simultaneous notes, as objects on their own(chords), and then considers the horizontal relations between them (e.g., harmoniccadences).

Hidden layer Any neuron layer located between the input layer and the outputlayer of a neural network architecture.

Hold The information about a note that extends its duration over a single time step.

Hyperparameter Higher-order parameters about the configuration of a neural net-work architecture and its behavior. Examples are: number of layers, number of neu-rons for each layer, learning rate and stride (for a convolutional architecture).

Input layer The first layer of a neural network architecture. It is an interface con-sisting in a set of nodes without internal computation.

Input manipulation strategy A strategy for generating content based on the in-cremental modification of a representation to be processed by an artificial neuralnetwork architecture.

268 Glossary

Iterative feedforward strategy A strategy for generating content by generating itssuccessive time slices.

Latent variable In statistics, a variable which is not directly observed. In deeplearning architectures, variables within a hidden layer. By sampling a latent vari-able(s), one may control the generation, e.g., in the case of a variational autoencoder.

Layer A component of a neural network architecture composed of a set of neuronswith no direct connexions between them.

Linear regression In statistics, linear regression is an approach for modeling the(assumed linear) relationship between a scalar variable and one or several explana-tory variable(s).

Linear separability The ability to separate by a line or a hyperplane the elementsof two different classes represented in an Euclidian space.

Long short-term memory (LSTM) A type of recurrent neural network architec-ture with capacity for learning long term correlations and not suffering from thevanishing or exploding gradient problem during the training phase. The idea is tosecure information in memory cells protected from the standard data flow of therecurrent network. Decisions about writing to, reading from and forgetting the val-ues of cells are performed by the opening or closing of gates and are expressed at adistinct control level, while being learnt during the training process.

Many-hot encoding Strategy used to encode simultaneously several values of acategorical variable, e.g., a triadic chord composed of three note pitches. As for aone-hot encoding, it is based on a vector having as its length the number of pos-sible values (e.g., from C4 to B4). Each occurrence of a note is represented with acorresponding 1 with all other elements being 0.

Markov chain A stochastic model describing a sequence of possible states. Thechance to change from the current state to a state or to another state is governed bya probability and does not depend on previous states.

Melody The abbreviation of a single-voice monophonic melody, that is a sequenceof notes for a single instrument with at most one note at the same time.

Musical instrument digital interface (MIDI) A technical standard that describesa protocol, a digital interface and connectors for interoperability between variouselectronic musical instruments, softwares and devices.

Multilayer Perceptron (MLP) A feedforward neural architecture composed ofsuccessive layers, with at least one hidden layer.

Multivoice (aka Multitrack) The abbreviation of a multivoice polyphony, that isa set of sequences of notes intended for more than one voice or instrument.

Neuron The atomic processing element (unit) of an artificial neural network ar-chitecture, inspired by the biological model of a neuron. A neuron has several inputconnexions, each one with an associated weight, and one output. A neuron will com-

Glossary 269

pute the weighted sum of all its input values and then apply its associated activationfunction in order to compute its output value. Weights will be adjusted during thetraining phase of the neural network architecture.

Node The atomic structural element of an artificial neural network architecture. Anode could be a processing unit (a neuron) or a simple interface element for a value,e.g., in the case of the input layer or a bias node.

Nonlinear function A function used as an activation function in an artificial neuralnetwork architecture in order to introduce nonlinearity and to address the linearseparability limitation.

Objective The nature and the destination of the musical content to be generated bya neural network architecture. Examples of objectives are: a monophonic melody tobe played by a human flutist and a polyphonic accompaniment played by a synthe-sizer.

One-hot encoding Strategy used to encode a categorical variable (e.g., a notepitch) as a vector having as its length the number of possible values (e.g., fromC4 to B4). A given element (e.g., a note pitch) is represented with a corresponding1 with all other elements being 0. The name comes from digital circuits, one-hotreferring to a group of bits among which the only legal (possible) combinations ofvalues are those with a single high (hot) (1) bit, all the others being low (0).

Output layer The last layer of a neural network architecture. It includes the outputactivation function which could be for instance a sigmoid or a softmax in the caseof a classification task.

Overfitting The situation for an artificial neural network architecture (and moregenerally speaking for a machine learning algorithm) when the model learnt is wellfit to the training data but not to the evaluation data. This means the inability of themodel to generalize well.

Parameter The parameters of an artificial neural network architecture are theweights associated to each connexion between neurons as well as the biases as-sociated to each layer.

Perceptron One of the first artificial neural network architecture, created by Rosen-blatt in 1957. It had no hidden layer and suffered from the linear separability limi-tation.

Piano roll Representation of a melody (monophonic or polyphonic) inspired fromautomated pianos. Each “perforation” represents a note control information, to trig-ger a given note. The length of the perforation corresponds to the duration of a note.In the other dimension, the localization (height) of a perforation corresponds to itspitch.

Pitch class The name of the corresponding note (e.g., C) independently of the oc-tave position. Also named chroma.

270 Glossary

Polyphony The abbreviation of a single-voice polyphony, that is a sequence ofnotes for a single instrument (e.g., a guitar or a piano) with possibly simultaneousnotes.

Pooling For a convolutional architecture, a data dimensionality reduction operation(by max, average or sum) for each feature map produced by a convolutional stage,while retaining significant information. Pooling brings the important property of theinvariance to small transformations, distortions and translations in the input image.

Pre-training A technique, also named greedy layer-wise unsupervised training,consisting in prior training in cascade (one layer at a time) of each hidden layer.It turned out to be a significant improvement for the accurate training of artificialneural networks with several layers by initializing the weights based on learnt data.

Q-learning An algorithm for reinforcement learning based on an incremental re-finement of the action value function Q which represents the cumulated rewards fora given state and a given action.

Recurrent connexion A connexion from an output of a node to its input. By exten-sion, a layer recurrent connexion fully connects all layer nodes outputs to all nodesinputs. This is the basis of a recurrent neural network (RNN) architecture.

Recurrent neural network (RNN) A type of artificial neural network architecturewith recurrent connexions. It is used to learn sequences.

Reinforcement learning An area of machine learning concerned with an agentmaking successive decisions about an action in an environment while receiving areward (reinforcement signal) after each action. The objective for the agent is tofind the best policy maximizing its cumulated rewards.

Reinforcement strategy A strategy for content generation by modeling generationof successive notes as a reinforcement learning problem while using an RNN as areference for the modeling of the reward. Therefore, one may introduce arbitrarycontrol objectives (e.g., adherence to current tonality, maximum number of repeti-tions, etc.) as additional reward terms.

ReLU The rectified linear unit function, which may be used as a hidden layer non-linear activation function, specially in the case of convolutions.

Representation The nature and format of the information (data) used to train andto generate musical content. Examples of types of representation are: signal, spec-trum, piano roll and MIDI.

Rest The information about the absence of a note (silence) during one (or more)time step(s).

Restricted Boltzmann machine (RBM) A specific type of artificial neural net-work that can learn a probability distribution over its set of inputs. It is stochastic,has no output and uses a specific learning algorithm.

Glossary 271

Sampling The action of producing an item (a sample) according to a given proba-bility distribution over the possible values. As more and more samples are generated,their distribution should more closely approximate the given distribution.

Sampling strategy A strategy for generating content where variables of a contentrepresentation are incrementally instantiated and refined according to a target prob-ability distribution which has been previously learnt.

Seed-based generation An approach to generate arbitrary content (e.g., a longmelody) with a minimal (seed) information (e.g., a first note).

Self-supervised learning A category of machine learning when the output value ofthe example (target value of the supervision) is equal to the input value. An exampleis the training of an autoencoder.

Sigmoid Also named the logistic function, it is used as an output layer activationfunction for binary classification tasks and it may also be used as a hidden layernon-linear activation function.

Single-step feedforward strategy A strategy for generating content where a feed-forward architecture processes in a single processing step a global temporal scoperepresentation which includes all time slices.

Softmax Generalization of the sigmoid (logistic) function to the case of multipleclasses. Used as an output activation function for multiclass single-label classifica-tion.

Sparse autoencoder An autoencoder with a sparsity constraint such that its hiddenlayer units are inactive most of the time. The objective is to enforce the specializa-tion of each unit in the hidden layer as a specific feature detector.

Spectrogram A visual representation of a spectrum of an audio signal obtained viaa Fourier transform.

Stacked autoencoder A set of hierarchically nested autoencoders with decreasingnumbers of hidden layer units.

Strategy The way the architecture will process representations in order to generatethe objective while matching desired requirements. Examples of types of strategyare: single-step feedforward, iterative feedforward and decoder feedforward.

Stride For a convolutional architecture, the number of pixels by which we slide thefilter matrix over the input matrix.

Style transfer The technique for capturing a style (e.g., of a given painting, by cap-turing the correlations between neurons for each layer) and applying it onto anothercontent.

Supervised learning A category of machine learning where for each training ex-ample a target information (a scalar value in case of a regression and a class in caseof a classification) is provided.

272 Glossary

Support vector machine (SVM) A class of supervised machine learning modelsfor linear classification with optimization of the separation margin. A kernel methodis usually associated to a SVM in order to transform the initial nonlinear classifica-tion problem into a linear classification problem within a higher dimension space.

Tanh (aka Hyperbolic tangent) The hyperbolic tangent function, which may beused as a hidden layer non-linear activation function.

Test set (aka Validation set) The subset of examples (dataset) which are used forevaluating the ability of the learnt model to generalize, that is to predict or to classifyproperly in the presence of yet unseen data.

Time slice The time interval considered as an atomic portion (grain) of the tempo-ral representation used by an artificial neural network architecture.

Time step The atomic increment of time considered by an artificial neural networkarchitecture.

Training set The subset of examples (dataset) which are used for training the arti-ficial neural network architecture.

Transfer learning An area of machine learning concerned with the ability to reusewhat has been learnt and apply (transfer) it to related domains or tasks.

Turing test Initially codified in 1950 by Alan Turing and named by him the “im-itation game”, the “Turing test” is a test of the ability for a machine to exhibit in-telligent behavior equivalent to (and more precisely, indistinguishable from) the be-havior of a human. In his imaginary experimental setting, Turing proposed the testto be a natural language conversation between a human (the evaluator) and a hiddenactor (another human or a machine). If the evaluator cannot reliably tell the machinefrom the human, the machine is said to have passed the test.

Unit See neuron.

Unit selection strategy A strategy for content generation about querying succes-sive musical units (e.g., one measure long melody segments) from a database andconcatenating them in order to generate a sequence according to some user charac-teristics.

Unsupervised learning A category of machine learning which extracts informa-tion from data without any added label or class information.

Variational autoencoder (VAE) An autoencoder with the added constraint thatthe encoded representation (its latent variables) follow some prior probability dis-tribution, usually a Gaussian distribution. The variational autoencoder is thereforeable to learn a “smooth” latent space mapping to realistic examples which providesinteresting ways to control the variation of the generation.

Value encoding The direct encoding of a numerical value as a scalar.

Glossary 273

Vanishing or exploding gradient problem A known problem when training a re-current neural network caused by the difficulty of estimating gradients, because,in backpropagation through time, recurrence brings repetitive multiplications andcould thus lead to over amplify or minimize effects (numerical errors). The longshort-term memory (LSTM) architecture solved the problem.

Waveform The raw representation of a signal as the evolution of its amplitude intime.

Weight A numerical parameter associated to a connexion between a node (neuronor not) and a unit (neuron). A neuron will compute the weighted sum of the acti-vations of its connexions and then apply its associated activation function. Weightswill be adjusted during the training phase.

Zero-padding For a convolutional architecture, the padding of the input matrixwith zeros around its border.

Index

ABC notation, 32, 48, 135, 263Abstraction, 1Accent, 187Accompaniment, 16, 116, 219, 243, 263Accurate, 192Action, 107

evaluation, 108selection, 108

Activation, 179, 181function, xxvii, 59, 64, 78, 81, 263

Ad hoc, 113, 130, 147Adaptation, 108, 217AF, see Activation function, 59Agent, 107, 108Agnostic, 5AI, see Artificial intelligence, 4, 218, 246Alan Turing, 3AlexNet, 52Algorithm, 195Algorithmic composition, 2, 7, 263Analysis, 223ANN, see Artificial neural networkAnomaly detection, 2Anticipation-RNN, 103, 109, 157, 163, 171,

224Architectural, 109, 163

meta-level, 81pattern, 66, 102, 109

Architecture, vii, 12, 55, 115, 263Argmax, 71, 73, 131, 157Argsort, 74Art, 208, 248Artificial

intelligence, xxvii, 4, 51, 218, 246neural network, see Neural network, 1, 52,

263AST, see Audio style transfer, 224

Asymmetry, 129, 166Attention mechanism, 98, 99, 112, 245, 264Attribute, 87, 157, 159, 161, 204

vector arithmetics, 87, 204Audio, 20, 21, 41, 102, 166, 196

style transfer, xxviiAudioWord2Vec, 112Autoencoder, 2, 36, 40, 65, 82, 85, 89, 90, 107,

109, 111, 121, 243, 245, 264Autoencoder(RNN, RNN), 109, 111Automated, 17Autonomous, 17Average, 87, 204Axis, 151Axone, 59

Bach, 3, 4, 125, 134, 149, 170, 211, 213, 247BachBot, 34, 218, 224, 247Backpropagation, 51, 79, 96, 98, 99, 177, 181,

264through time, xxvii, 96, 98

Backward, 212Bag-of-words, xxvii, 40, 193, 264BALSTM, see Bi-Axial LSTM, 153Bar, 27Baroque, 170Basic building block, 62, 67Bass, 213

line, 47, 103, 163, 164Beat, 27, 103, 163, 164Beethoven, 171Bernoulli, 92Bi-Axial LSTM, xxvii, 153, 170, 171, 224Bias, 22, 53, 56, 62, 264

node, 56, 264Bidirectional, 109, 144

LSTM, xxvii, 143

275J.-P. Briot et al., Deep Learning Techniques for Music Generation, Computational

Synthesis and Creative Systems, https://doi.org/10.1007/978-3-319-70163-9

© Springer Nature Switzerland AG 2020

276 Index

recurrent neural network, 110, 161, 173,202, 212

RNN, see Bidirectional recurrent neuralnetwork, 110

Bill Evans, 199Bin, 44, 45, 171Binary, 28, 42

cross-entropy, 72, 78Binning, 44, 202, 264Biological

inspiration, 56, 59neural network, 56

Black box, 218Block, see LSTM block

Gibbs sampling, 124, 126, 149BLSTM, see Bidirectional LSTM, 110, 127,

143, 147, 173, 212, 224, 241Blues, 127BluesM , 224BluesMC , 224Boltzmann machine, 90Boolean, 42, 91, 92Bossa nova, 137Bottleneck hidden layer, 89, 121, 177, 264Bottom-up, 6, 13, 192BOW, see Bag-of-words, 40, 193, 264BPTT, see Backpropagation through time, 96Brittle, 5Bucketing, 44

C-RBM, see Convolutional restricted Boltz-mann machine, 92, 102, 109, 125, 156,187, 196, 201, 224, 244

C-RNN-GAN, 104, 109, 110, 161, 173, 212,224, 244

Cadence, 147, 212CAN, see Creative adversarial networks, 208Case-based reasoning, xxvii, 137Categorical, 42, 91

cross-entropy, 72, 77Causal convolution, 166CBR, see Case-based reasoning, 137Cell, see LSTM cellCeltic, 48, 135, 224Cepstrum, 21Chain rule, 79Challenge, vii, 12, 13, 115, 120, 264CHORAL, 3Chorale, 16, 116, 149, 211, 213Chord, 16, 26, 34, 40, 124, 143, 147

progression, 16, 34, 103, 143, 163Chord2Vec, 34Chroma, see Chromagram, 264Chromagram, 23, 264

Classical, 48, 149, 152, 201Classical piano MIDI database, 48, 152–154Classification, 1, 2, 65, 71, 106, 116, 264

task, 45, 131ClockworkRNN, 206CNN, see Convolutional neural network, 99Cocktail party effect, 41Coherence, 17, 47Column vector, 57Composer, 170Composition, 109

style transfer, 186, 195Compound architecture, 108, 125, 264Computer music, 3, 7Concatenation, 192, 194

cost, 192, 194CONCERT, 210, 224, 244Conditional

architecture, see Conditioning architecture,163

probability, 85, 95, 148, 157, 173, 213Conditioning, 103, 163, 164, 166, 168, 171,

196, 208architecture, 103, 163, 265input, 103, 104, 109, 112, 113, 163, 164,

166, 171Conditioning(RNN, RNN), 109Connexion, 81, 265Consonant, 177Constrained sampling, xxvii, 156, 187, 188Constraint, 156, 173, 186

satisfaction, 189Content, 2, 116

generation, 2Context, 161, 246, 248Continuous, 20, 42, 92Contrastive divergence, 91, 187Control, 81, 103, 108, 124, 137, 192, 195, 207,

215interface, 17parameter, 208

Convergence, 189Convex, 55, 79ConvNet, see Convolutional neural network,

99Convolution, 1, 99, 103, 166, 208, 244, 265Convolutional, 102

architecture, 244network, see Convolutional neural network,

102, 104, 166, 245neural network, xxvii, 52, 99restricted Boltzmann machine, xxvii, 187

Convolutional(RBM), 109Convolved feature, 100

Index 277

Corpus, 2, 5, 192Correlation, 100, 180, 181, 219, 265Cost, 54, 55, 79, 84, 85, 194

function, 72, 109, 179Counterpoint, 16, 116, 117, 147, 177, 213,

219, 265Country, 144Couple, 148Coverage, 17Creative, 208

adversarial networks, xxvii, 208Creativity, 7, 162, 170, 207, 248Criterium, 192, 193Cross-entropy, 72, 85, 265

cost, 72, 112, 150, 175CS, see Constrained sampling, 187CSV, see Comma-separated valuesCumulated rewards, 108Cyber-Joao, 137, 198

Data synthesis, 81, 265Database, 192, 195Dataset, 37, 47, 48, 116, 178, 192, 217, 266

augmentation, 47, 81dBFS, see Decibel relative to full scale, 23Decibel, 25

relative to full scale, xxvii, 23Decision tree, 44Decoder, 83, 90, 109, 111, 121, 266

feedforward strategy, 121, 127, 157, 244,266

Decomposition, 23Deep, 69

belief net, 52learning, vii, 1, 62, 218, 266network, see Deep neural network, 89neural network, 108, 266reinforcement learning, 107, 108

Deep Dream, 177, 178, 222deepAutoController, 123, 215, 224DeepBach, 39, 40, 113, 117, 125, 157, 159,

174, 177, 210, 211, 215, 218, 219, 222,224, 241, 243, 246, 247

DeepHear, 36, 121, 177, 224, 244, 246DeepHearC , 177, 224DeepHearM , 123, 224DeepJ, 45, 103, 153, 154, 163, 170, 196, 224Dendrite, 59Depth, 68, 100Destination, 15Deterministic, 91, 156Dilated convolution, 166Discrete, 20, 42Discretization, 37, 171

Discriminator, 105, 107, 208, 266Disentanglement, 196

learning, 196Distance, 54, 177, 187, 193Distribution, see Probability distribution, 124,

137, 187, 208Double Q-learning, 108Dropout, 81Drums, 46, 164Duration, 30, 33DX7, 2Dynamics, 41, 136, 137

Early stopping, 81Embedding, 83, 90, 103, 121, 163, 171, 177,

193–195, 202, 266Emergence, 179EMI, see Experiments in musical intelligence,

3Emulative, 208Encapsulate, 111Encoder, 83, 89, 107, 109, 111, 266Encoding, 40, 42, 72, 83, 90, 111, 266End-to-end architecture, 22, 266Energy, 92Engineering, 59Enharmony, 19, 40, 266Entangled, 41Entanglement, 196Entropy, 76Entry point, 155Environment, 107, 108Equiprobable, 209Equivariance, 101Error, 79Estimation, 54, 79, 105, 108, 187, 190Evaluation, 66, 195, 214, 247Event message, 29Expectation, 77Experience, 65Experiments in musical intelligence, xxvii, 3Explainability, 218Explanatory variable, 53Exploding gradient problem, 98, 273Exploration, 188

exploitation dilemma, 108Expressiveness, 41, 136Extensional, 133, 168, 170Extraction, 19, 65, 137, 192

Fast, 245Fourier transform, xxvii, 123

Feature, 19, 40, 89, 121, 192, 193, 208-based representation, 40

278 Index

detector, 84, 100extraction, 40, 83, 89, 193extractor, 193map, 100, 266matching, 106, 162, 208

Feedback, 108, 192, 217Feedforward, 36, 62, 116, 121, 181, 267

network, see Feedforward neural network,113, 120, 164, 178, 245

neural network, 67, 78, 116, 243propagation, 78

Fermata, 38, 213, 219FFT, see Fast Fourier transformFill, 192Filter, 100Fine-grained, 194Fixed-length, 111Flow, 151Flow Machines, 36, 48, 199FlowComposer, 5, 199Flute, 16FM, see Frequency modulation, 2Folk, 48, 135, 144, 149, 192

-rnn, 33, 135Form, 186, 201Forward, 212Fourier transform, 19, 23, 123, 267Frequency, 25

modulation, xxvii, 2

Gain, 65, 108, 190Game theory, 105GAN, see Generative adversarial networks,

104, 107, 109, 110, 157, 161, 208, 267GAN(RNN, RNN), 109GarageBand, 3Gated recurrent unit, xxvii, 98Gaussian distribution, 85GD, see Gradient descentGenerality, 5Generalization, 5, 47, 54, 79, 217

error, 80Generate, 116

-and-test, 124, 156Generated data, 20, 36Generation, 2, 5, 103, 108, 163, 166, 187, 217

data, 20, 36phase, 19

Generativeadversarial networks, xxvii, 104, 157, 161,

208, 267latent optimization, xxvii, 106model, 85, 90, 157, 161

Generator, 104, 208, 267

Genre, see Musical genre, 170Geodesic latent space regularization, xxvii,

158Gibbs sampling, xxvii, 85, 92, 124, 188, 213GLO, see Generative latent optimization, 106Global, 186

conditioning, 166, 171minimum, 55

GLSR, see Geodesic latent space regulariza-tion, 158

GLSR-VAE, 112, 158, 178, 224, 244GoogLeNet, 69GPU, see Graphics processing unit, 1, 64Gradient, 55, 79, 181, 267

ascent, 179descent, xxvii, 55, 66, 177, 267

Grammar, 4, 5Granularity, 192Graphics processing unit, xxvii, 1, 64Greedy layer-wise unsupervised training, 52Grid search, 219GRU, see Gated recurrent unit, 98GS, see Gibbs sampling, 92, 124, 188Guitar, 16, 137

Handcrafted, 193feature, 40, 134model, 5

Harmonics, 23, 38Harmonization, 199, 212Harmony, 16, 125, 147, 151, 267Hertz, 25Heterogeneous, 47, 108Heuristic, 55, 194Hexahedria, 224Hidden

layer, 51, 67, 93, 121, 267layer unit, 89Markov model, xxvii, 146unit, see Hidden layer unit

Hierarchical, 1, 89, 112, 187, 202, 206High-level, 179, 189Higher

-order, 187level, 89

History, 245HMM, see Hidden Markov model, 146Hold, 38, 39, 159, 174, 267Homogeneous, 108Hook, 155Hyperbolic tangent, 60, 272Hyperparameter, 79, 81, 100, 106, 157, 219,

267Hypothesis, 53

Index 279

Hz, see Hertz

Identification, 2Identity, 83, 85Illiac Suite, 2Image, 2, 48, 99, 177, 178, 180, 244

recognition, 1, 52, 98Incremental, 108, 180, 243Index, 93, 193, 195Initialization, 55Innermost hidden layer, 89, 264Input, 19

layer, 62, 67, 103, 163, 267manipulation strategy, 177, 185, 195, 267node, 42, 56, 62, 82variable, 42

Instantiate, 109Instrument, 16, 103, 163, 166Integer, 42Integration, 150Intensional, 168Interactive, 17, 215Interface, 121Interpolation, 87, 204Interval, 26Invariance, 101, 187, 245Iterative feedforward strategy, 36, 127, 138,

147, 156, 195, 210, 222, 244, 268

Jazz, 16, 27, 48, 144, 192, 201Jitter, 179JSB Chorales dataset, 48, 153

Kernel, 100Key, 47KL-divergence, see Kullback-Leibler

divergence, 77Knowledge representation, 20Kullback-Leibler divergence, xxvii, 77

L2, 81Label, 40, 65, 83, 97, 103, 121, 163, 177, 195Language, 111Latent

space, 85, 87, 244variable, 83–85, 87, 244, 268

Layer, 1, 55, 67, 68, 78, 245, 268Lead sheet, 16, 34, 48Lead sheet data base, xxvii, 48Learning, 2, 5, 108, 217

rate, 55, 81Length, 111, 126Likelihood, 78Limitation, vii, 120

Linearalgebra, 56, 64regression, 2, 53, 268separability, 67, 268

Localconditioning, 166minimum, 79

Logisticfunction, see Sigmoid functionregression, 2, 59, 71

Long-term dependency, 98, 99short-term memory, xxvii, 1, 52, 98, 268

Loss, 54Lossy representation, 40Low-level, 189LSDB, see Lead sheet data base, 36, 48LSTM, see Long short-term memory, 1, 52,

98, 99, 113, 201, 245, 268Lyrics, 16, 34

Machine learning, xxviii, 1Major, 27, 187Manifold, 85

learning, 83, 85Many-hot encoding, 43, 45–47, 168, 268Markov

chain, 2, 189, 199, 207, 268constraint, 189

Matrix, 57, 63, 64, 78Max/MSP, 2Maximize, 177Maximum likelihood estimation, 78Mean squared error, xxviii, 54, 72Measure, 27, 33, 245Mel-frequency cepstral coefficients, xxvii, 21Melody, see Single-voice monophonic melody,

34, 116, 125, 147, 268Memory, 80, 98, 152, 168

-based, 80Meta-level, 81, 98Metadata, 32, 38, 213Meter, 27, 32, 186, 187Metropolis-Hastings, 124MFCC, see Mel-frequency cepstral

coefficients, 21Michel Legrand, 196, 199MIDI, see Musical instrument digital interface,

2, 17, 29, 38, 40, 171, 268note number, 29, 42note velocity, 29

MidiNet, 20, 27, 30, 36, 103, 104, 106, 162,163, 167, 224, 244, 245

Miles Davis, 192

280 Index

MiniBach, 36, 117, 147, 177, 210, 211, 218,219, 224, 243

Minibatch, 217gradient descent, 55

Minimax, 105Minor, 27, 187MIR, see Music information retrieval, 6Misclassification, 106ML, see Machine learning, 1MLP, see Multilayer Perceptron, 78, 268MNIST, see Modified National Institute of

Standards and Technology, 48, 86Modality, 103, 163Mode, 15, 187Model, 53, 55Modified National Institute of Standards and

Technology, xxviiiModularity, 163Monophonic, 16, 43

melody, see Single-voice monophonicmelody

Motif, 178, 179, 187, 201, 245Mozart, 3, 187MSE, see Mean squared errorMulti

-many-hot encoding, 43-one-hot encoding, 43, 45multiclass single label, 73

Multiclassmultilabel, 73single label, 73

Multicriteria, 195, 247Multilayer

neural network, see Neural networkPerceptron, xxviii, 78, 268

Multinomial, 92Multinoulli, 91, 92Multiple linear regression, 53Multitrack, see Multivoice polyphony, 28, 30,

43, 268polyphony, see Multivoice polyphony

Multivariate linear regression, 57Multivoice, see Multivoice polyphony, 28, 43,

219, 268polyphony, 16, 218

MuseData library, 48, 153, 154Music, 2

information retrieval, xxviii, 6style transfer, 185unit, 192

Music I, 2Musical

content, viigenre, 5, 103, 123, 163

instrument digital interface, xxvii, 2, 29, 268unit, 192

MusicNet dataset, 48MusicTransformer, 245MusicVAE, 47, 110, 112, 178, 202, 224, 244MusicXML, 34

Nash equilibrium, 105Natural language processing, xxviii, 34, 40, 98Nested, 109Neural

net, see Neural networknetwork, xxviii, 51, 62, 104, 115, 116, 218Turing machine, xxviii, 98

Neuron, 56, 268NLP, see Natural language processing, 40NN, see Neural networkNode, 56, 269Nonlinear, 71

function, 59, 269Norm, 208Normal distribution, 85Notation convention, 27, 32, 34, 53, 60, 63, 69,

71, 78, 85, 93, 115, 228, 236Note, 16, 25, 34, 113, 124

beginning, 39duration, 37, 117ending, 38, 39onset, 41, 168, 187, 198step, 36, 133tie, 38

Nottingham database, 48, 153NTM, see Neural Turing machine, 98Nuance, 136

Objective, vii, 11, 15, 20, 116, 208, 269destination, 15facet, 15mode, 15type, 15use, 15

Octave, 23, 25, 153One-hot encoding, 42, 43, 45, 46, 71, 269OpenMusic, 5Optimization, 66, 81Organization, 201Originality, 207Output, 19

activation function, 71, 72layer, 62, 67, 269layer activation function, see Output

activation functionnode, 62, 82

Overestimation, 108

Index 281

Overfitting, 54, 81, 217, 269

Parallel, 166Parameter, 53, 81, 269

initialization, 55sharing, 101

Parameterization, 121Pareidolia, 178Pattern, see Architectural pattern, 187

instantiation, 109PCA, see Principal component analysis, 83Perceptron, 51, 69, 78, 269Percussion, 46Performance, 41, 49, 137, 195

style transfer, 195Performance RNN, 41, 44, 137, 224Piano, 16, 149, 152

roll, 30, 38, 43, 269Pitch, 25, 29, 30, 32, 42, 103, 149, 245

class, 23, 26, 32, 144, 269notation, 25

Pivot representation, 111Pixel, 179Plagiarism, 8, 122Policy, 65, 108Polymorphism, 20Polyphonic, 16Polyphony, see Single-voice polyphony, 113,

270Pooling, 101, 166, 270Pop, 144, 167Positional constraint, 157, 163, 173Pre-training, 1, 52, 55, 91, 270Prediction, 1, 2, 54, 62, 65, 71, 115, 116Principal component analysis, xxviii, 83Probability, 53, 71

distribution, 53, 71, 77, 85, 90, 95, 124, 134Process, 194Profile, 187Propagation, 152Pseudo-Gibbs sampling, 213Psychedelic, 178

Q-learning, 108, 270-table, 108function, 108network, 190

Quantization, 41, 136Query, 192, 195

R&B, see Rhythm and bluesRadial function, 69Ragtime, 121, 177

Random, 55, 121, 135, 156, 177, 180noise, 179

Randomness, 137Range, 92Rank, 194, 195RBM, see Restricted Boltzmann machine, 65,

90, 92, 109, 113, 125, 127, 156, 270RBMC , 224Real, 92ReChord, 199Recopy, 207Rectified linear unit, xxviii, 60Recurrent, 102

connexion, 93, 270highway network, xxviii, 175network, see Recurrent neural network, 52,

65, 103, 104, 111, 113, 156, 245neural network, xxviii, 36, 93, 125, 243,

244, 270Recursion, 97, 127, 138, 147Referential, 223Refinement, 109Regression, 2, 65, 71Regularization, 81, 208Reinforcement

learning, xxviii, 65, 107, 270signal, 107strategy, 189, 192, 270

Relation, 223Relationship, 115Relevance, 193ReLU, see Rectified linear unit, 60, 101, 270Rendering, 199Repetition, 138Replay, 108Representation, vii, 1, 12, 42, 55, 66, 117, 134,

270learning, 85

ResNet, 69Rest, 25, 159, 270Restricted Boltzmann machine, xxviii, 2, 90,

125, 156, 270Retrieval, 137Reuse, 245Reverse, 168Reward, 65, 107, 108, 190, 192, 218RHN, see Recurrent highway network, 175Rhythm, 27, 164, 224Rhythmic pattern, 137Richard Feynman, 3RL, see Reinforcement learning, 107RL-Tuner, 107, 190, 201, 218, 224RNN, see Recurrent neural network, 93, 102,

103, 109–111, 125, 243, 244, 270

282 Index

RNN Encoder-Decoder, 34, 108, 109, 111,147, 198, 244, 245

RNN-DBN, 150RNN-RBM, 109, 113, 125, 148, 151, 224Robustness, 45, 101Rock, 143, 192Row vector, 57Rule, 2, 5, 137

-based system, 4, 5

Saliency map, 221Sample, 91, 104, 106, 124, 156SampleRNN, 206Sampling, 71, 74, 78, 85, 90, 124, 149, 156,

243, 271strategy, 125, 134, 185, 210, 213, 222, 271

Scalar, 42, 43Scale, 187Sceptrum, 21Scope, 17Score, 25, 195Search, 186Seed, 90, 120, 121, 127, 128

-based generation, 127, 147, 243, 271Selection, 192Selective Gibbs sampling, xxviii, 188Self

-information, 75-similarity, 187-supervised learning, 83, 121, 193, 271

Semantic relevance, 192, 193Sense of direction, 192, 201Sequence, 16, 111, 125

-to-sequence learning, 111Sequencer, 17Sequential, 127, 141, 224SGD, see Stochastic gradient descent, 55, 66,

79SGS, see selective Gibbs sampling, 188Sigmoid, 60, 71, 271Signal, 12, 21, 23

processing, 20Similarity, 123, 177, 187, 207Simple linear regression, 53Simulated annealing, 188Simultaneous, 161Single

-step, 116-step feedforward strategy, 36, 116, 120,

210, 243, 271-track polyphony, see Single-voice

polyphony, 46, 47-voice monophonic melody, 16-voice polyphony, 16, 218

Sinusoidal, 23Size, 47Slice, see Time sliceSoftmax, 45, 46, 71, 271Solo, 192Sonata, 187Sound, 195Sparse autoencoder, 84, 109, 121, 271Sparsity, 17, 48, 84, 187Speaker, 166Specialization, 109, 246Spectrogram, 23, 271Spectrum, 19, 23Stacked autoencoder, 89, 108, 109, 271State, 107Step, 36, 91, 95Stochastic, 2, 91, 124, 156

gradient descent, xxviii, 55, 66, 79music, 3

Strategy, viii, 12, 13, 114, 115, 156, 271Stride, 100, 271Structure, 81, 186, 187, 192, 201

imposition, 196Style, 2, 5, 15, 103, 163, 170, 171, 180, 192,

208imposition, 177transfer, 177, 180, 184, 195, 246, 271

Sub-symbolic, 4, 218Subsampling, 101Successor semantic relevance, 194Summary, 223Supervised learning, 65, 79, 83, 91, 97, 116,

120, 271Support vector machine, xxviii, 52, 272SVM, see Support vector machine, 52, 272Symbolic, 4, 20, 51, 196

representation, 19Symbolic Music dataset, 48Symmetric, 83, 110, 173Synthesis, 2Synthesizer, 2Synthetic data, 47System, 11, 115

Tab, 30, 36, 48Tablature, 30Tag, 103, 113, 163, 166, 209Tanh, 60, 272Target, 65, 177Task, 2, 11, 246Tchaikovsky, 170Templagiarism, 186Template, 186Tempo, 34, 41, 136

Index 283

Temporalscope, 36, 219sequence, 93, 113

Ternary, 28Test

data, 19set, 80, 272

Text, 2, 32, 40, 47-to-speech, xxviii, 166, 192

Textual representation, 32Texture, 179TheoryTab database, 48Threshold, 59Tick, 29Tied, 38

note, 193, 218Timbre, 196

style transfer, 195, 196Time, 36, 93, 244

-delay neural network, 102frame, 34, 218quantization, 48signature, 27, 187slice, 36, 272step, 36, 37, 39, 99, 104, 164, 166, 171, 235,

243, 272stretching, 41

Time-Windowed, 139, 224, 241Timing, 137Tonality, 186Top-down, 192Track, 16, 29, 43, 47Trade-off, 162Training, 54, 79, 106, 166, 217, 245

corpus, 207data, 19error, 80phase, 19set, 80, 217, 272

Transcription, 125, 192Transfer learning, 52, 177, 184, 245, 272Transformer, 99, 245Transition, 192, 193Translation, 1, 2, 99, 111, 244Transposition, 47

invariance, 153Triad, 26, 144TTS, see Text-to-speech, 166, 192Tuple, 193Turing, see Alan Turing

test, 3, 105, 214, 247, 272Typology, viii

Unfolded, 93

Unit, 56, 59, 92, 272selection strategy, 192, 201, 272

UnitSelection, 224Universal approximator, 67Unsupervised learning, 65, 83, 91, 272Use, 15User, 192

-defined, 170interface, 124, 215

VAE, see Variational autoencoder, 85, 107,109, 110, 112, 157, 196, 272

Validationdata, 19set, 80, 82, 272

Value encoding, 42, 45, 46, 272Vanishing gradient problem, 98, 273Variable, 19, 53

length, 111, 147, 243Variance, 188Variational, 112

autoencoder, xxviii, 85, 89, 109, 110, 112,157, 178, 196, 244, 272

recurrent autoencoder, xxviii, 158, 202recurrent autoencoder supported by history,

xxviii, 175Variational(Autoencoder(RNN, RNN)), 112Vectorized, 64Velocity, 29, 38, 41Video game, 158Visible unit, 92Visual, 178Vocabulary, 33Vocal, 16Voice, 16, 43, 47, 147, 213Volume, 29, 41VRAE, see Variational recurrent autoencoder,

147, 158, 161, 178, 202, 224, 244VRASH, see Variational recurrent autoencoder

supported by history, 113, 163, 175, 224

Waltz, 27Waveform, 19, 21, 166, 273WaveNet, 20, 45, 102–104, 113, 163, 164, 166,

171, 206, 224, 244, 245Web, 214Weight, 53, 79, 81, 98, 273

decay, 81Weighted sum, 59Window, 187Word embedding, 40Word2Vec, 34, 40

Xenakis, 3

284 Index

XML, 144

Yamaha e-Piano Competition dataset, 49

Zero-padding, 100, 273